c++boost.gifHermitian Matrix

Hermitian Matrix

Description

The templated class hermitian_matrix<T, F1, F2, A> is the base container adaptor for hermitian matrices. For a (n x n)-dimensional hermitian matrix and 0 <= i < n, 0 <= j < n holds hi, j = hj, i-. The storage of hermitian matrices is packed.

Example

int main () {

    using namespace boost::numeric::ublas;

    hermitian_matrix<std::complex<double>, lower> ml (3, 3);

    for (int i = 0; i < ml.size1 (); ++ i) 

        for (int j = 0; j <= i; ++ j)

            ml (i, j) = std::complex<double> (3 * i + j, 3 * i + j);

    std::cout << ml << std::endl;

    hermitian_matrix<std::complex<double>, upper> mu (3, 3);

    for (int i = 0; i < m.size1 (); ++ i) 

        for (int j = i; j < m.size2 (); ++ j)

            mu (i, j) = std::complex<double> (3 * i + j, 3 * i + j);

    std::cout << mu << std::endl;

}

Definition

Defined in the header hermitian.hpp.

Template parameters

Parameter Description Default
T The type of object stored in the matrix.  
F1 Functor describing the type of the hermitian matrix. [1] lower
F2 Functor describing the storage organization. [2] row_major
A The type of the adapted array. [3] unbounded_array<T>

Model of

Matrix.

Type requirements

None, except for those imposed by the requirements of Matrix.

Public base classes

matrix_expression<hermitian_matrix<T, F1, F2, A> >

Members

Member Description
hermitian_matrix () Allocates an uninitialized hermitian_matrix that holds zero rows of zero elements.
hermitian_matrix (size_type size) Allocates an uninitialized hermitian_matrix that holds size rows of size elements.
hermitian_matrix (const hermitian_matrix &m) The copy constructor.
template<class AE>
hermitian_matrix (const matrix_expression<AE> &ae)
The extended copy constructor.
void resize (size_type size) Reallocates a hermitian_matrix to hold size rows of size elements. The content of the hermitian_matrix is not preserved.
size_type size1 () const Returns the number of rows.
size_type size2 () const Returns the number of columns.
const_reference operator () (size_type i, size_type j) const Returns a const reference of the j-th element in the i-th row.
reference operator () (size_type i, size_type j) Returns a reference of the j-th element in the i-th row.
hermitian_matrix &operator = (const hermitian_matrix &m) The assignment operator.
hermitian_matrix &assign_temporary (hermitian_matrix &m) Assigns a temporary. May change the hermitian matrix m.
template<class AE>
hermitian_matrix &operator = (const matrix_expression<AE> &ae)
The extended assignment operator.
template<class AE>
hermitian_matrix &assign (const matrix_expression<AE> &ae)
Assigns a matrix expression to the hermitian matrix. Left and right hand side of the assignment should be independent.
template<class AE>
hermitian_matrix &operator += (const matrix_expression<AE> &ae)
A computed assignment operator. Adds the matrix expression to the hermitian matrix.
template<class AE>
hermitian_matrix &plus_assign (const matrix_expression<AE> &ae)
Adds a matrix expression to the hermitian matrix. Left and right hand side of the assignment should be independent.
template<class AE>
hermitian_matrix &operator -= (const matrix_expression<AE> &ae)
A computed assignment operator. Subtracts the matrix expression from the hermitian matrix.
template<class AE>
hermitian_matrix &minus_assign (const matrix_expression<AE> &ae)
Subtracts a matrix expression from the hermitian matrix. Left and right hand side of the assignment should be independent.
template<class AT>
hermitian_matrix &operator *= (const AT &at)
A computed assignment operator. Multiplies the hermitian matrix with a scalar.
template<class AT>
hermitian_matrix &operator /= (const AT &at)
A computed assignment operator. Divides the hermitian matrix through a scalar.
void swap (hermitian_matrix &m) Swaps the contents of the hermitian matrices.
void insert (size_type i, size_type j, const_reference t) Inserts the value t at the j-th element of the i-th row.
void erase (size_type i, size_type j) Erases the value at the j-th elemenst of the i-th row.
void clear () Clears the matrix.
const_iterator1 begin1 () const Returns a const_iterator1 pointing to the beginning of the hermitian_matrix.
const_iterator1 end1 () const Returns a const_iterator1 pointing to the end of the hermitian_matrix.
iterator1 begin1 () Returns a iterator1 pointing to the beginning of the hermitian_matrix.
iterator1 end1 () Returns a iterator1 pointing to the end of the hermitian_matrix.
const_iterator2 begin2 () const Returns a const_iterator2 pointing to the beginning of the hermitian_matrix.
const_iterator2 end2 () const Returns a const_iterator2 pointing to the end of the hermitian_matrix.
iterator2 begin2 () Returns a iterator2 pointing to the beginning of the hermitian_matrix.
iterator2 end2 () Returns a iterator2 pointing to the end of the hermitian_matrix.
const_reverse_iterator1 rbegin1 () const Returns a const_reverse_iterator1 pointing to the beginning of the reversed hermitian_matrix.
const_reverse_iterator1 rend1 () const Returns a const_reverse_iterator1 pointing to the end of the reversed hermitian_matrix.
reverse_iterator1 rbegin1 () Returns a reverse_iterator1 pointing to the beginning of the reversed hermitian_matrix.
reverse_iterator1 rend1 () Returns a reverse_iterator1 pointing to the end of the reversed hermitian_matrix.
const_reverse_iterator2 rbegin2 () const Returns a const_reverse_iterator2 pointing to the beginning of the reversed hermitian_matrix.
const_reverse_iterator2 rend2 () const Returns a const_reverse_iterator2 pointing to the end of the reversed hermitian_matrix.
reverse_iterator2 rbegin2 () Returns a reverse_iterator2 pointing to the beginning of the reversed hermitian_matrix.
reverse_iterator2 rend2 () Returns a reverse_iterator2 pointing to the end of the reversed hermitian_matrix.

Notes

[1] Supported parameters for the type of the hermitian matrix are lower and upper.

[2] Supported parameters for the storage organization are row_major and column_major.

[3] Supported parameters for the adapted array are unbounded_array<T>, bounded_array<T> and std::vector<T>.

Interface

    // Array based hermitian matrix class 

    template<class T, class F1, class F2, class A>

    class hermitian_matrix: 

        public matrix_expression<hermitian_matrix<T, F1, F2, A> > {

    public:      

        typedef std::size_t size_type;

        typedef std::ptrdiff_t difference_type;

        typedef T value_type;

        typedef const T const_reference;

        typedef T &reference;

        typedef const T *const_pointer;

        typedef T *pointer;

        typedef F1 functor1_type;

        typedef F2 functor2_type;

        typedef A array_type;

        typedef const A const_array_type;

        typedef const hermitian_matrix<T, F1, F2, A> const_self_type;

        typedef hermitian_matrix<T, F1, F2, A> self_type;

        typedef const matrix_const_reference<const_self_type> const_closure_type;

        typedef matrix_reference<self_type> closure_type;

        typedef packed_tag storage_category;

        typedef typename F1::packed_category packed_category;

        typedef typename F2::orientation_category orientation_category;



        // Construction and destruction

        hermitian_matrix ();

        hermitian_matrix (size_type size);

        hermitian_matrix (size_type size1, size_type size2);

        hermitian_matrix (const hermitian_matrix &m);

        template<class AE>

        hermitian_matrix (const matrix_expression<AE> &ae);



        // Accessors

        size_type size1 () const;

        size_type size2 () const;

        const_array_type &data () const;

        array_type &data ();



        // Resizing

        void resize (size_type size);

        void resize (size_type size1, size_type size2);



        // Element access

        const_reference operator () (size_type i, size_type j) const;

        reference operator () (size_type i, size_type j);



        // Assignment

        hermitian_matrix &operator = (const hermitian_matrix &m);

        hermitian_matrix &assign_temporary (hermitian_matrix &m);

        template<class AE>

        hermitian_matrix &operator = (const matrix_expression<AE> &ae);

        template<class AE>

        hermitian_matrix &reset (const matrix_expression<AE> &ae);

        template<class AE>

        hermitian_matrix &assign (const matrix_expression<AE> &ae);

        template<class AE>

        hermitian_matrix& operator += (const matrix_expression<AE> &ae);

        template<class AE>

        hermitian_matrix &plus_assign (const matrix_expression<AE> &ae);

        template<class AE>

        hermitian_matrix& operator -= (const matrix_expression<AE> &ae);

        template<class AE>

        hermitian_matrix &minus_assign (const matrix_expression<AE> &ae);

        template<class AT>

        hermitian_matrix& operator *= (const AT &at);

        template<class AT>

        hermitian_matrix& operator /= (const AT &at);



        // Swapping

        void swap (hermitian_matrix &m);

        friend void swap (hermitian_matrix &m1, hermitian_matrix &m2);



        // Element insertion and erasure

        void insert (size_type i, size_type j, const_reference t);

        void erase (size_type i, size_type j);

        void clear ();



        class const_iterator1;

        class iterator1;

        class const_iterator2;

        class iterator2;

        typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;

        typedef reverse_iterator_base1<iterator1> reverse_iterator1;

        typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;

        typedef reverse_iterator_base2<iterator2> reverse_iterator2;



        // Element lookup

        const_iterator1 find_first1 (int rank, size_type i, size_type j) const;

        iterator1 find_first1 (int rank, size_type i, size_type j);

        const_iterator1 find_last1 (int rank, size_type i, size_type j) const;

        iterator1 find_last1 (int rank, size_type i, size_type j);

        const_iterator2 find_first2 (int rank, size_type i, size_type j) const;

        iterator2 find_first2 (int rank, size_type i, size_type j);

        const_iterator2 find_last2 (int rank, size_type i, size_type j) const;

        iterator2 find_last2 (int rank, size_type i, size_type j);



        // Iterators simply are indices.



        class const_iterator1:

            public container_const_reference<hermitian_matrix>,

            public random_access_iterator_base<const_iterator1, value_type> {

        public:

            typedef packed_random_access_iterator_tag iterator_category;

            typedef typename hermitian_matrix::difference_type difference_type;

            typedef typename hermitian_matrix::value_type value_type;

            typedef typename hermitian_matrix::const_reference reference;

            typedef typename hermitian_matrix::const_pointer pointer;

            typedef const_iterator2 dual_iterator_type;

            typedef const_reverse_iterator2 dual_reverse_iterator_type;



            // Construction and destruction

            const_iterator1 ();

            const_iterator1 (const hermitian_matrix &m, size_type it1, size_type it2);

            const_iterator1 (const iterator1 &it);



            // Arithmetic

            const_iterator1 &operator ++ ();

            const_iterator1 &operator -- ();

            const_iterator1 &operator += (difference_type n);

            const_iterator1 &operator -= (difference_type n);

            difference_type operator - (const const_iterator1 &it) const;



            // Dereference

            reference operator * () const;



            const_iterator2 begin () const;

            const_iterator2 end () const;

            const_reverse_iterator2 rbegin () const;

            const_reverse_iterator2 rend () const;



            // Indices

            size_type index1 () const;

            size_type index2 () const;



            // Assignment 

            const_iterator1 &operator = (const const_iterator1 &it);



            // Comparison

            bool operator == (const const_iterator1 &it) const;

            bool operator < (const const_iterator1 &it) const;

        };



        const_iterator1 begin1 () const;

        const_iterator1 end1 () const;



        class iterator1:

            public container_reference<hermitian_matrix>,

            public random_access_iterator_base<iterator1, value_type> {

        public:

            typedef packed_random_access_iterator_tag iterator_category;

            typedef typename hermitian_matrix::difference_type difference_type;

            typedef typename hermitian_matrix::value_type value_type;

            typedef typename hermitian_matrix::reference reference;

            typedef typename hermitian_matrix::pointer pointer;

            typedef iterator2 dual_iterator_type;

            typedef reverse_iterator2 dual_reverse_iterator_type;



            // Construction and destruction

            iterator1 ();

            iterator1 (hermitian_matrix &m, size_type it1, size_type it2);



            // Arithmetic

            iterator1 &operator ++ ();

            iterator1 &operator -- ();

            iterator1 &operator += (difference_type n);

            iterator1 &operator -= (difference_type n);

            difference_type operator - (const iterator1 &it) const;



            // Dereference

            reference operator * () const;



            iterator2 begin () const;

            iterator2 end () const;

            reverse_iterator2 rbegin () const;

            reverse_iterator2 rend () const;



            // Indices

            size_type index1 () const;

            size_type index2 () const;



            // Assignment 

            iterator1 &operator = (const iterator1 &it);



            // Comparison

            bool operator == (const iterator1 &it) const;

            bool operator < (const iterator1 &it) const;

        };



        iterator1 begin1 ();

        iterator1 end1 ();



        class const_iterator2:

            public container_const_reference<hermitian_matrix>,

            public random_access_iterator_base<const_iterator2, value_type> {

        public:

            typedef packed_random_access_iterator_tag iterator_category;

            typedef typename hermitian_matrix::difference_type difference_type;

            typedef typename hermitian_matrix::value_type value_type;

            typedef typename hermitian_matrix::const_reference reference;

            typedef typename hermitian_matrix::const_pointer pointer;

            typedef const_iterator1 dual_iterator_type;

            typedef const_reverse_iterator1 dual_reverse_iterator_type;



            // Construction and destruction

            const_iterator2 ();

            const_iterator2 (const hermitian_matrix &m, size_type it1, size_type it2);

            const_iterator2 (const iterator2 &it);



            // Arithmetic

            const_iterator2 &operator ++ ();

            const_iterator2 &operator -- ();

            const_iterator2 &operator += (difference_type n);

            const_iterator2 &operator -= (difference_type n);

            difference_type operator - (const const_iterator2 &it) const;



            // Dereference

            reference operator * () const;



            const_iterator1 begin () const;

            const_iterator1 end () const;

            const_reverse_iterator1 rbegin () const;

            const_reverse_iterator1 rend () const;



            // Indices

            size_type index1 () const;

            size_type index2 () const;



            // Assignment 

            const_iterator2 &operator = (const const_iterator2 &it);



            // Comparison

            bool operator == (const const_iterator2 &it) const;

            bool operator < (const const_iterator2 &it) const;

        };



        const_iterator2 begin2 () const;

        const_iterator2 end2 () const;



        class iterator2:

            public container_reference<hermitian_matrix>,

            public random_access_iterator_base<iterator2, value_type> {

        public:

            typedef packed_random_access_iterator_tag iterator_category;

            typedef typename hermitian_matrix::difference_type difference_type;

            typedef typename hermitian_matrix::value_type value_type;

            typedef typename hermitian_matrix::reference reference;

            typedef typename hermitian_matrix::pointer pointer;

            typedef iterator1 dual_iterator_type;

            typedef reverse_iterator1 dual_reverse_iterator_type;



            // Construction and destruction

            iterator2 ();

            iterator2 (hermitian_matrix &m, size_type it1, size_type it2);



            // Arithmetic

            iterator2 &operator ++ ();

            iterator2 &operator -- ();

            iterator2 &operator += (difference_type n);

            iterator2 &operator -= (difference_type n);

            difference_type operator - (const iterator2 &it) const;



            // Dereference

            reference operator * () const;



            iterator1 begin () const;

            iterator1 end () const;

            reverse_iterator1 rbegin () const;

            reverse_iterator1 rend () const;



            // Indices

            size_type index1 () const;

            size_type index2 () const;



            // Assignment 

            iterator2 &operator = (const iterator2 &it);



            // Comparison

            bool operator == (const iterator2 &it) const;

            bool operator < (const iterator2 &it) const;

        };



        iterator2 begin2 ();

        iterator2 end2 ();



        // Reverse iterators



        const_reverse_iterator1 rbegin1 () const;

        const_reverse_iterator1 rend1 () const;



        reverse_iterator1 rbegin1 ();

        reverse_iterator1 rend1 ();



        const_reverse_iterator2 rbegin2 () const;

        const_reverse_iterator2 rend2 () const;



        reverse_iterator2 rbegin2 ();

        reverse_iterator2 rend2 ();

    };

Hermitian Adaptor

Description

The templated class hermitian_adaptor<M, F> is a hermitian matrix adaptor for other matrices.

Example

int main () {

    using namespace boost::numeric::ublas;

    matrix<std::complex<double> > m (3, 3);

    hermitian_adaptor<matrix<std::complex<double> >, lower> hal (m);

    for (int i = 0; i < hal.size1 (); ++ i) 

        for (int j = 0; j <= i; ++ j)

            hal (i, j) = std::complex<double> (3 * i + j, 3 * i + j);

    std::cout << hal << std::endl;

    hermitian_adaptor<matrix<std::complex<double> >, upper> hau (m);

    for (int i = 0; i < hau.size1 (); ++ i) 

        for (int j = i; j < hau.size2 (); ++ j)

            hau (i, j) = std::complex<double> (3 * i + j, 3 * i + j);

    std::cout << sau << std::endl;

}

Definition

Defined in the header hermitian.hpp.

Template parameters

Parameter Description Default
M The type of the adapted matrix.  
F Functor describing the type of the hermitian adaptor. [1] lower

Model of

Matrix Expression.

Type requirements

None, except for those imposed by the requirements of Matrix Expression.

Public base classes

matrix_expression<hermitian_adaptor<M, F> >

Members

Member Description
hermitian_adaptor () Constructs a hermitian_adaptor that holds zero rows of zero elements.
hermitian_adaptor (matrix_type &data) Constructs a hermitian_adaptor of a matrix.
hermitian_adaptor (const hermitian_adaptor &m) The copy constructor.
template<class AE>
hermitian_adaptor (const matrix_expression<AE> &ae)
The extended copy constructor.
size_type size1 () const Returns the number of rows.
size_type size2 () const Returns the number of columns.
const_reference operator () (size_type i, size_type j) const Returns a const reference of the j-th element in the i-th row.
reference operator () (size_type i, size_type j) Returns a reference of the j-th element in the i-th row.
hermitian_adaptor &operator = (const hermitian_adaptor &m) The assignment operator.
hermitian_adaptor &assign_temporary (hermitian_adaptor &m) Assigns a temporary. May change the hermitian adaptor m.
template<class AE>
hermitian_adaptor &operator = (const matrix_expression<AE> &ae)
The extended assignment operator.
template<class AE>
hermitian_adaptor &assign (const matrix_expression<AE> &ae)
Assigns a matrix expression to the hermitian adaptor. Left and right hand side of the assignment should be independent.
template<class AE>
hermitian_adaptor &operator += (const matrix_expression<AE> &ae)
A computed assignment operator. Adds the matrix expression to the hermitian adaptor.
template<class AE>
hermitian_adaptor &plus_assign (const matrix_expression<AE> &ae)
Adds a matrix expression to the hermitian adaptor. Left and right hand side of the assignment should be independent.
template<class AE>
hermitian_adaptor &operator -= (const matrix_expression<AE> &ae)
A computed assignment operator. Subtracts the matrix expression from the hermitian adaptor.
template<class AE>
hermitian_adaptor &minus_assign (const matrix_expression<AE> &ae)
Subtracts a matrix expression from the hermitian adaptor. Left and right hand side of the assignment should be independent.
template<class AT>
hermitian_adaptor &operator *= (const AT &at)
A computed assignment operator. Multiplies the hermitian adaptor with a scalar.
template<class AT>
hermitian_adaptor &operator /= (const AT &at)
A computed assignment operator. Divides the hermitian adaptor through a scalar.
void swap (hermitian_adaptor &m) Swaps the contents of the hermitian adaptors.
const_iterator1 begin1 () const Returns a const_iterator1 pointing to the beginning of the hermitian_adaptor.
const_iterator1 end1 () const Returns a const_iterator1 pointing to the end of the hermitian_adaptor.
iterator1 begin1 () Returns a iterator1 pointing to the beginning of the hermitian_adaptor.
iterator1 end1 () Returns a iterator1 pointing to the end of the hermitian_adaptor.
const_iterator2 begin2 () const Returns a const_iterator2 pointing to the beginning of the hermitian_adaptor.
const_iterator2 end2 () const Returns a const_iterator2 pointing to the end of the hermitian_adaptor.
iterator2 begin2 () Returns a iterator2 pointing to the beginning of the hermitian_adaptor.
iterator2 end2 () Returns a iterator2 pointing to the end of the hermitian_adaptor.
const_reverse_iterator1 rbegin1 () const Returns a const_reverse_iterator1 pointing to the beginning of the reversed hermitian_adaptor.
const_reverse_iterator1 rend1 () const Returns a const_reverse_iterator1 pointing to the end of the reversed hermitian_adaptor.
reverse_iterator1 rbegin1 () Returns a reverse_iterator1 pointing to the beginning of the reversed hermitian_adaptor.
reverse_iterator1 rend1 () Returns a reverse_iterator1 pointing to the end of the reversed hermitian_adaptor.
const_reverse_iterator2 rbegin2 () const Returns a const_reverse_iterator2 pointing to the beginning of the reversed hermitian_adaptor.
const_reverse_iterator2 rend2 () const Returns a const_reverse_iterator2 pointing to the end of the reversed hermitian_adaptor.
reverse_iterator2 rbegin2 () Returns a reverse_iterator2 pointing to the beginning of the reversed hermitian_adaptor.
reverse_iterator2 rend2 () Returns a reverse_iterator2 pointing to the end of the reversed hermitian_adaptor.

Notes

[1] Supported parameters for the type of the hermitian adaptor are lower and upper.

Interface

    // Hermitian matrix adaptor class 

    template<class M, class F>

    class hermitian_adaptor: 

        public matrix_expression<hermitian_adaptor<M, F> > {

    public:      

        typedef const M const_matrix_type;

        typedef M matrix_type;

        typedef F functor_type;

        typedef typename M::size_type size_type;

        typedef typename M::difference_type difference_type;

        typedef typename M::value_type value_type;

        typedef typename M::value_type const_reference;

        typedef typename M::reference reference;

        typedef typename M::const_pointer const_pointer;

        typedef typename M::pointer pointer;

        typedef const hermitian_adaptor<M, F> const_self_type;

        typedef hermitian_adaptor<M, F> self_type;

        typedef const matrix_const_reference<const_self_type> const_closure_type;

        typedef matrix_reference<self_type> closure_type;

        typedef typename storage_restrict_traits<typename M::storage_category,

                                                 packed_proxy_tag>::storage_category storage_category;

        typedef typename F::packed_category packed_category;

        typedef typename M::orientation_category orientation_category;



        // Construction and destruction

        hermitian_adaptor ();

        hermitian_adaptor (matrix_type &data);

        hermitian_adaptor (const hermitian_adaptor &m);



        // Accessors

        size_type size1 () const;

        size_type size2 () const;

        const_matrix_type &data () const;

        matrix_type &data ();



        // Element access

        const_reference operator () (size_type i, size_type j) const;

        reference operator () (size_type i, size_type j);



        // Assignment

        hermitian_adaptor &operator = (const hermitian_adaptor &m);

        hermitian_adaptor &assign_temporary (hermitian_adaptor &m);

        template<class AE>

        hermitian_adaptor &operator = (const matrix_expression<AE> &ae);

        template<class AE>

        hermitian_adaptor &assign (const matrix_expression<AE> &ae);

        template<class AE>

        hermitian_adaptor& operator += (const matrix_expression<AE> &ae);

        template<class AE>

        hermitian_adaptor &plus_assign (const matrix_expression<AE> &ae);

        template<class AE>

        hermitian_adaptor& operator -= (const matrix_expression<AE> &ae);

        template<class AE>

        hermitian_adaptor &minus_assign (const matrix_expression<AE> &ae);

        template<class AT>

        hermitian_adaptor& operator *= (const AT &at);

        template<class AT>

        hermitian_adaptor& operator /= (const AT &at);



        // Swapping

        void swap (hermitian_adaptor &m);

        friend void swap (hermitian_adaptor &m1, hermitian_adaptor &m2);



        class const_iterator1;

        class iterator1;

        class const_iterator2;

        class iterator2;

        typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;

        typedef reverse_iterator_base1<iterator1> reverse_iterator1;

        typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;

        typedef reverse_iterator_base2<iterator2> reverse_iterator2;



        // Element lookup

        const_iterator1 find_first1 (int rank, size_type i, size_type j) const;

        iterator1 find_first1 (int rank, size_type i, size_type j);

        const_iterator1 find_last1 (int rank, size_type i, size_type j) const;

        iterator1 find_last1 (int rank, size_type i, size_type j);

        const_iterator2 find_first2 (int rank, size_type i, size_type j) const;

        iterator2 find_first2 (int rank, size_type i, size_type j);

        const_iterator2 find_last2 (int rank, size_type i, size_type j) const;

        iterator2 find_last2 (int rank, size_type i, size_type j);



        // Iterators simply are indices.



        class const_iterator1:

            public container_const_reference<hermitian_adaptor>,

            public random_access_iterator_base<const_iterator1, value_type> {

        public:

            typedef packed_random_access_iterator_tag iterator_category;

            typedef typename hermitian_adaptor::difference_type difference_type;

            typedef typename hermitian_adaptor::value_type value_type;

            typedef typename hermitian_adaptor::const_reference reference;

            typedef typename hermitian_adaptor::const_pointer pointer;

            typedef const_iterator2 dual_iterator_type;

            typedef const_reverse_iterator2 dual_reverse_iterator_type;



            // Construction and destruction

            const_iterator1 ();

            const_iterator1 (const hermitian_adaptor &m, size_type it1, size_type it2);

            const_iterator1 (const iterator1 &it);



            // Arithmetic

            const_iterator1 &operator ++ ();

            const_iterator1 &operator -- ();

            const_iterator1 &operator += (difference_type n);

            const_iterator1 &operator -= (difference_type n);

            difference_type operator - (const const_iterator1 &it) const;



            // Dereference

            reference operator * () const;



            const_iterator2 begin () const;

            const_iterator2 end () const;

            const_reverse_iterator2 rbegin () const;

            const_reverse_iterator2 rend () const;



            // Indices

            size_type index1 () const;

            size_type index2 () const;



            // Assignment 

            const_iterator1 &operator = (const const_iterator1 &it);



            // Comparison

            bool operator == (const const_iterator1 &it) const;

            bool operator < (const const_iterator1 &it) const;

        };



        const_iterator1 begin1 () const;

        const_iterator1 end1 () const;



        class iterator1:

            public container_reference<hermitian_adaptor>,

            public random_access_iterator_base<iterator1, value_type> {

        public:

            typedef packed_random_access_iterator_tag iterator_category;

            typedef typename hermitian_adaptor::difference_type difference_type;

            typedef typename hermitian_adaptor::value_type value_type;

            typedef typename hermitian_adaptor::reference reference;

            typedef typename hermitian_adaptor::pointer pointer;

            typedef iterator2 dual_iterator_type;

            typedef reverse_iterator2 dual_reverse_iterator_type;



            // Construction and destruction

            iterator1 ();

            iterator1 (hermitian_adaptor &m, size_type it1, size_type it2);



            // Arithmetic

            iterator1 &operator ++ ();

            iterator1 &operator -- ();

            iterator1 &operator += (difference_type n);

            iterator1 &operator -= (difference_type n);

            difference_type operator - (const iterator1 &it) const;



            // Dereference

            reference operator * () const;



            iterator2 begin () const;

            iterator2 end () const;

            reverse_iterator2 rbegin () const;

            reverse_iterator2 rend () const;



            // Indices

            size_type index1 () const;

            size_type index2 () const;



            // Assignment 

            iterator1 &operator = (const iterator1 &it);



            // Comparison

            bool operator == (const iterator1 &it) const;

            bool operator < (const iterator1 &it) const;

        };



        iterator1 begin1 ();

        iterator1 end1 ();



        class const_iterator2:

            public container_const_reference<hermitian_adaptor>,

            public random_access_iterator_base<const_iterator2, value_type> {

        public:

            typedef packed_random_access_iterator_tag iterator_category;

            typedef typename hermitian_adaptor::difference_type difference_type;

            typedef typename hermitian_adaptor::value_type value_type;

            typedef typename hermitian_adaptor::const_reference reference;

            typedef typename hermitian_adaptor::const_pointer pointer;

            typedef const_iterator1 dual_iterator_type;

            typedef const_reverse_iterator1 dual_reverse_iterator_type;



            // Construction and destruction

            const_iterator2 ();

            const_iterator2 (const hermitian_adaptor &m, size_type it1, size_type it2);

            const_iterator2 (const iterator2 &it);



            // Arithmetic

            const_iterator2 &operator ++ ();

            const_iterator2 &operator -- ();

            const_iterator2 &operator += (difference_type n);

            const_iterator2 &operator -= (difference_type n);

            difference_type operator - (const const_iterator2 &it) const;



            // Dereference

            reference operator * () const;



            const_iterator1 begin () const;

            const_iterator1 end () const;

            const_reverse_iterator1 rbegin () const;

            const_reverse_iterator1 rend () const;



            // Indices

            size_type index1 () const;

            size_type index2 () const;



            // Assignment 

            const_iterator2 &operator = (const const_iterator2 &it);



            // Comparison

            bool operator == (const const_iterator2 &it) const;

            bool operator < (const const_iterator2 &it) const;

        };



        const_iterator2 begin2 () const;

        const_iterator2 end2 () const;



        class iterator2:

            public container_reference<hermitian_adaptor>,

            public random_access_iterator_base<iterator2, value_type> {

        public:

            typedef packed_random_access_iterator_tag iterator_category;

            typedef typename hermitian_adaptor::difference_type difference_type;

            typedef typename hermitian_adaptor::value_type value_type;

            typedef typename hermitian_adaptor::reference reference;

            typedef typename hermitian_adaptor::pointer pointer;

            typedef iterator1 dual_iterator_type;

            typedef reverse_iterator1 dual_reverse_iterator_type;



            // Construction and destruction

            iterator2 ();

            iterator2 (hermitian_adaptor &m, size_type it1, size_type it2);



            // Arithmetic

            iterator2 &operator ++ ();

            iterator2 &operator -- ();

            iterator2 &operator += (difference_type n);

            iterator2 &operator -= (difference_type n);

            difference_type operator - (const iterator2 &it) const;



            // Dereference

            reference operator * () const;



            iterator1 begin () const;

            iterator1 end () const;

            reverse_iterator1 rbegin () const;

            reverse_iterator1 rend () const;



            // Indices

            size_type index1 () const;

            size_type index2 () const;



            // Assignment 

            iterator2 &operator = (const iterator2 &it);



            // Comparison

            bool operator == (const iterator2 &it) const;

            bool operator <(const iterator2 &it) const;

        };



        iterator2 begin2 ();

        iterator2 end2 ();



        // Reverse iterators



        const_reverse_iterator1 rbegin1 () const;

        const_reverse_iterator1 rend1 () const;



        reverse_iterator1 rbegin1 ();

        reverse_iterator1 rend1 ();



        const_reverse_iterator2 rbegin2 () const;

        const_reverse_iterator2 rend2 () const;



        reverse_iterator2 rbegin2 ();

        reverse_iterator2 rend2 ();

    };

Copyright (©) 2000-2002 Joerg Walter, Mathias Koch
Permission to copy, use, modify, sell and distribute this document is granted provided this copyright notice appears in all copies. This document is provided ``as is'' without express or implied warranty, and with no claim as to its suitability for any purpose.

Last revised: 8/3/2002